Object, mesh, material, material slot, face, material assignment: How do they work all together?
Questions


Q1. Slots can be stored at Object or Mesh level to suit your needs.
Q2. Slots color faces. Slots at the Mesh Data level can be shared. 
Q3. I do not believe your statement is true in all cases. I reordered slots and did not see same result as stated in your question.
Your probably know this. You can switch to shared data by choosing the existing data item.  You can stop sharing by clicking on the number which is greater than 1 in the mesh data panel, seen in the image below.  The image above shows Duplicate and Duplicate Linked.  The User Preferences can also fine tune these settings.  A Blender Material contains a sequence of slots which can be assigned to faces.